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Консультация № 186048
15.05.2012, 21:30
78.80 руб.
15.05.2012, 21:42
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Обсуждение
15.05.2012, 22:38
общий
это ответ
Здравствуйте, Максим!
Для функции arctg x разложение в степенной ряд (ряд Тейлора) имеет вид:
для всех |x| < 1. Соответственно, для f(x) = arctg x[sup]2[/sup] будем иметь
При почленном интегрировании последнего ряда получаем
При x = 0 все члены ряда равны 0, поэтому значение определённого интеграла находим, подставляя в выражение для ряда x = 0.5:
Для функции arctg x разложение в степенной ряд (ряд Тейлора) имеет вид:
для всех |x| < 1. Соответственно, для f(x) = arctg x[sup]2[/sup] будем иметь
При почленном интегрировании последнего ряда получаем
При x = 0 все члены ряда равны 0, поэтому значение определённого интеграла находим, подставляя в выражение для ряда x = 0.5:
Форма ответа
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